Whats the problem? i cant solve it w/o the problem doll
The third option I believe
Tangent always meets radius at 90° angle.
Angle ABC = 90° so Pythagoras' theorem applies.
r² + 4² = (r+2)²
r² + 16 = r² + 4r + 4
12 = 4r
r = 3
Explanation:
Basically, you can do it in many ways. But just, in my opinion, exactly linear algebra was made for such cases.
the optimal way is to do it with Cramer's rule.
First, find the determinant and then find the determinant x, y, v, u.
Afterward, simply divide the determinant of variables by the usual determinant.
eg.
and etc.
I think that is the best way to solve it without a hustle of myriad of calculations reducing it to row echelon form and solving with Gaussian elimination.
Answer: Choice D.
Max: f (-1,-2)=4; min:f(3,5)=-11
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Work Shown:
Plug in (x,y) = (-1,3)
f(x,y) = -2x-y
f(-1,3) = -2*(-1)-3
f(-1,3) = 2-3
f(-1,3) = -1
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Plug in (x,y) = (3,5)
f(x,y) = -2x-y
f(3,5) = -2*3-5
f(3,5) = -6-5
f(3,5) = -11
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Plug in (x,y) = (4,-1)
f(x,y) = -2x-y
f(4,-1) = -2*4-(-1)
f(4,-1) = -8+1
f(4,-1) = -7
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Plug in (x,y) = (-1,-2)
f(x,y) = -2x-y
f(-1,-2) = -2*(-1)-(-2)
f(-1,-2) = 2+2
f(-1,-2) = 4
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The four outputs are: -1, -11, -7, and 4
The largest output is 4 and that happens when (x,y) = (-1,-2)
So the max is f(x,y) = 4
The smallest output is -11 and that happens when (x,y) = (3,5)
So the min is f(x,y) = -11
This all points to choice D being the answer.